If you have given stiffness matrix then how to find flexibility mateix
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about the stiffness matrix.
In short, a column of K matrix represent the nodal loads that needs to be applied to maintain a certain deformation - Let me explain it with examples :
Let us consider the following bar element
1, 2 represent the node numbers. u’s are the nodal degrees of freedom and F’s are
nodal forces.
[K] {U} = F form for the bar is as follows :
Lets try to impose a specific deformation, set U1 = 1 and U2 =0 . The deformed bar looks like the following , we displace the node 1 by 1 unit and constraint the node 2.
Solving [K] {U} = F equation gives :
F1 = EA/ L and F2 = -EA/L
The other way of looking at it is ,
Can you observe that the first column of the stiffness matrix becomes the nodal load vector when you impose unit dof at the first node and zero at the other node ?
Like wise try imposing unit dof at the second node and zero at the first node i
In short, a column of K matrix represent the nodal loads that needs to be applied to maintain a certain deformation - Let me explain it with examples :
Let us consider the following bar element
1, 2 represent the node numbers. u’s are the nodal degrees of freedom and F’s are
nodal forces.
[K] {U} = F form for the bar is as follows :
Lets try to impose a specific deformation, set U1 = 1 and U2 =0 . The deformed bar looks like the following , we displace the node 1 by 1 unit and constraint the node 2.
Solving [K] {U} = F equation gives :
F1 = EA/ L and F2 = -EA/L
The other way of looking at it is ,
Can you observe that the first column of the stiffness matrix becomes the nodal load vector when you impose unit dof at the first node and zero at the other node ?
Like wise try imposing unit dof at the second node and zero at the first node i
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